We note that the Proca-Wentzel Lagrangian that we use is, in fact, equivalent to the Stückelberg Lagrangian when \(S(x)=0\)  (For the main references, see [1]}). Thus, our model coincides with that of Ref. [2]} (F1 above) when no Stückelberg field is present. An important difference between our model and a Stückelberg-like model is that the later predicts the existence of millicharged particles [3]}. That model introduces a new unit of electric charge, allowing the electric charge to have non-integer values. Hence, although both models have similar features there are many differences between the models.
